Benchmark West Texas Intermediate crude for July delivery rose 67 cents to close at US$98.44 a barrel on the New York Mercantile Exchange.
Brent crude, a benchmark for many international oil varieties, gained 55 cents to US$106.02 a barrel on the ICE Futures exchange in London.
The focus in oil markets, as in others, was on the Fed, as policy-makers began a two-day meeting.
To help support the U.S. economic recovery, the Fed has been buying $85 billion in bonds every month in an attempt to keep long-term interest rates low and encourage lending.
The new money generated has flowed into the financial system, helping many assets, including oil, to climb from the lows witnessed during the global recession following the 2008-2009 financial crisis.
After the meeting ends Wednesday, Fed chairman Ben Bernanke will hold a news conference. Investors want to hear if the Fed plans to reduce the amount of financial assets it is buying each month. Few expect a change in policy on Wednesday as some recent economic data has been disappointing. The uncertainty though has rattled markets in recent weeks.
Oil traders will also be monitoring fresh information on U.S. stockpiles of crude and refined products.
Data for the week ended June 14 is expected to show a decline of one million barrels in crude oil stocks and an increase of 1.2 million barrels in gasoline stocks, according to a survey of analysts by Platts, the energy information arm of McGraw-Hill.
The report on stockpiles from the U.S. Energy Department's Energy Information Administration — the market benchmark — is out on Wednesday.
In other energy futures trading on the Nymex, wholesale gasoline added two cents to US$2.88 a U.S. gallon (3.79 litres), heating oil was rose one cent to US$2.96 a gallon and natural gas gained three cents to US$3.91 per 1,000 cubic feet.
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